Performing a calibration process in a quantum computing system

ABSTRACT

In a general aspect, calibration is performed in a quantum computing system. In some cases, domains of a quantum computing system are identified, where the domains include respective domain control subsystems and respective subsets of quantum circuit devices in a quantum processor of the quantum computing system. Sets of measurements are obtained from one of the domains and stored in memory. Device characteristics of the quantum circuit devices of the domain are obtained based on the set of measurements, and the device characteristics are stored in a memory of the control system. Quantum logic control parameters for the subset of quantum circuit devices of the domain are obtained based on the set of measurements and stored in memory.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.16/841,300, entitled “Performing a Calibration Process in a QuantumComputing System,” and filed Apr. 6, 2020, which is a continuation ofU.S. patent application Ser. No. 16/390,964, entitled “Performing aCalibration Process in a Quantum Computing System.” and filed Apr. 22,2019, Now U.S. Pat. No. 10,643,143, which is a continuation of U.S.patent application Ser. No. 15/916,367, entitled “Performing aCalibration Process in a Quantum Computing System” and filed Mar. 9,2018, now U.S. Pat. No. 10,282,675, which claims priority to U.S.Provisional Application No. 62/469,648 entitled “Performing aCalibration Process in a Quantum Computing System” and filed Mar. 10,2017. The contents of all above-referenced priority applications arehereby incorporated by reference.

BACKGROUND

The following description relates to performing a calibration process ina quantum computing system.

In some quantum computing architectures, qubits are implemented insuperconducting circuits. The qubits can be implemented, for example, incircuit devices that include Josephson junctions. In some systems,circuit devices in a superconducting circuit are controlled by anexternal control module.

DESCRIPTION OF DRAWINGS

FIG. 1 is a block diagram of an example quantum computing system.

FIG. 2 is a block diagram of an example calibration process.

FIG. 3 is a block diagram of an example calibration process.

FIG. 4 is block diagram of an example quantum computing system.

FIG. 5 is a plot of a qubit frequency versus a flux pulse.

FIG. 6 is a diagram of an example gate tune-up process.

FIG. 7 is a diagram of an example process for flux bias automation(FBA).

DETAILED DESCRIPTION

In some aspects of what is described here, a calibration processprovides more efficient and accurate initialization of devices andoperations in a quantum computing system.

In some implementations, a calibration process provides automated system“bring-up” for a large-scale quantum computer system. As an example, thecalibration process may utilize design parameters, measured values, andautomatic optimization to determine operating parameters for amulti-qubit system after installing the system in an operatingenvironment (e.g., in a dilution refrigerator), so that the system canbe efficiently accessed as working or identified as sub-optimal. In somecases, complicated characterization processes can be divided intosub-processing units that can be scaled up and applied to large systems.For instance, defining a precise calibration sequence may allow rapidcharacterization of specialized processors.

In some implementations, a central computer process dispatches bring-upinstructions to several sub-processing units to assess a superconductingquantum circuit system. The sub-processing units can characterize thecircuit devices and tune up quantum logic gates for computation. Boththe characterization and the tune-up may follow a defined procedure. Bysubdividing bring-up tasks with a defined pass/fail criteria based ondesign and performance, a complex system can be brought up,characterized, and efficiently tuned-up.

FIG. 1 is a schematic diagram of an example quantum computing system100. The example quantum computing system 100 shown in FIG. 1 includes acontrol system 110, a signal delivery system 106, and a quantumprocessor cell 102. A quantum computing system may include additional ordifferent features, and the components of a quantum computing system mayoperate as described with respect to FIG. 1 or in another manner.

The example quantum computing system 100 shown in FIG. 1 can performquantum computational tasks by executing quantum algorithms. In someimplementations, the quantum computing system 100 can perform quantumcomputation by storing and manipulating information within individualquantum states of a composite quantum system. For example, qubits (i.e.,quantum bits) can be stored in and represented by an effective two-levelsub-manifold of a quantum coherent physical system. In some instances,quantum logic can be performed in a manner that allows large-scaleentanglement within the quantum system. Control signals can manipulatethe quantum states of individual qubits and the joint states of themultiple qubits. In some instances, information can be read out from thecomposite quantum system by measuring the quantum states of theindividual qubits.

In some implementations, the quantum computing system 100 can operateusing gate-based models for quantum computing. In some models,fault-tolerance can be achieved by applying a set of high-fidelitycontrol and measurement operations to the qubits. For example,topological quantum error correction schemes can operate on a lattice ofnearest-neighbor coupled qubits. In some instances, these and othertypes of quantum error correcting schemes can be adapted for a two- orthree-dimensional lattice of nearest neighbor coupled qubits, forexample, to achieve fault-tolerant quantum computation. Adjacent pairsof qubits in the lattice can be addressed, for example, with two-qubitlogic operations that are capable of generating entanglement,independent of other pairs in the lattice.

In some implementations, the quantum computing system 100 is constructedand operated according to a scalable quantum computing architecture. Forexample, in some cases, the architecture can be scaled to a large numberof qubits to achieve large-scale general purpose coherent quantumcomputing. In some instances, the architecture is adaptable and canincorporate a variety of modes for each technical component. Forexample, the architecture can be adapted to incorporate different typesof qubit devices, coupler devices, readout devices, signaling devices,etc.

In some instances, all or part of the quantum processor cell 102functions as a quantum processor, a quantum memory, or another type ofsubsystem. In some examples, the quantum processor cell includes aquantum circuit system. The quantum circuit system may include qubitdevices, resonator devices and possibly other devices that are used tostore and process quantum information. In some implementations, thequantum circuit system is a superconducting quantum circuit system, inwhich various circuit elements are capable of operating in asuperconducting state. In some implementations, the quantum circuitsystem is an integrated quantum circuit (e.g., an integratedsuperconducting quantum circuit).

In some implementations, the example quantum processor cell 102 canprocess quantum information by applying control signals to the qubitdevices or to the coupler devices housed in the quantum processor cell102. The control signals can be configured to encode information in thequbit devices, to process the information by performing quantum logicgates or other types of operations, or to extract information from thequbit devices. In some examples, the operations can be expressed assingle-qubit logic gates, two-qubit logic gates, or other types ofquantum logic gates that operate on one or more qubits. A sequence ofquantum logic operations can be applied to the qubits to perform aquantum algorithm. The quantum algorithm may correspond to acomputational task, a quantum error correction procedure, a quantumstate distillation procedure, or a combination of these and other typesof operations.

FIG. 1 shows an example quantum processor cell 102A that includes asuperconducting quantum circuit system 104. The example superconductingquantum circuit system 104 includes circuit devices 105 arranged in atwo-dimensional device array. Eight circuit devices are shown in FIG. 1. In some examples, some of the circuit devices 105 are qubit devicesthat each store a single qubit of information, and the qubits cancollectively represent the computational state of a quantum processor.In some cases, the superconducting quantum circuit system 104 mayinclude resonator devices coupled to the respective qubit devices, forinstance, where each qubit device includes a superconducting quantuminterference device (SQUID) loop and is capacitively coupled to aneighboring resonator device. The readout devices may be configured togenerate readout signals that indicate the computational state of thequantum processor or quantum memory. In some examples, some of thecircuit devices 105 are coupler devices that selectively operate onindividual qubits or pairs of qubits. For example, the coupler devicesmay produce entanglement or other multi-qubit states over two or morequbits. The superconducting quantum circuit system 104 may includeadditional devices (e.g., additional qubit devices, coupler devices andother types of devices).

The example quantum circuit system 104 also includes connections 103between neighboring pairs of the circuit devices 105. The connections103 can provide electromagnetic communication between the connectedcircuit devices. In some cases, the connections 103 are implemented ascapacitive or conductive connections. For instance, the connections 103may include metal traces, capacitors and other components. Thesuperconducting circuit devices 105 may be operated by microwave signalsdelivered in the quantum circuit system 104, for example, from thecontrol system 110. Signals may be exchanged among the circuit devices105 through the connections 103 or other signal pathways in the quantumcircuit system 104.

The circuit devices 105 in the quantum circuit system 104 may bearranged in one or more regular or irregular arrays. For instance, qubitdevices may be arranged in a rectilinear (e.g., rectangular or square)array that extends in two spatial dimensions (in the plane of the page),where each qubit device has four nearest-neighbor qubit devices. Qubitdevices can be arranged in another type of regular or irregular array(e.g., a hexagonal array). In some instances, the array of circuitdevices 204 also extends in a third spatial dimension (in/out of thepage), for example, to form a cubic array or another type of regular orirregular three-dimensional array.

The example quantum processor cell 102A includes multiple domains. InFIG. 1 , a first domain 101A and a second domain 101B are shown. Thequantum processor cell may include additional domains or different typesof domains. Each domain includes a subset of the circuit devices 105.For instance, the first domain 101A may include a first subset of qubitdevices, a first subset of coupler devices, and a first subset ofreadout devices, while the second domain 101B may include a secondsubset of qubit devices, a second subset of coupler devices, and asecond subset of readout devices. Each subset may include, for example,two, five, ten or more such devices. The domains may be defined byhardware, by control logic, by connections, by software or otherwise.

In the example shown in FIG. 1 , the signal delivery system 106 providescommunication between the control system 110 and the quantum processorcell 102. For example, the signal delivery system 106 can receivecontrol signals from the control system 110 and deliver the controlsignals to the quantum processor cell 102. In some instances, the signaldelivery system 106 performs preprocessing, signal conditioning, orother operations to the control signals before delivering them to thequantum processor cell 102.

In some instances, the signal delivery system 106 receives qubit readoutsignals from the quantum processor cell and delivers the qubit readoutsignals to the control system 110. In some instances, the signaldelivery system 106 performs preprocessing, signal conditioning or otheroperations on the readout signals before delivering them to the controlsystem 110. In some implementations, the signal delivery system 106includes include input and output processing hardware, input and outputconnections, and other components. The input and processing hardware mayinclude, for example, filters, attenuators, directional couplers,multiplexers, diplexers, bias components, signal channels, isolators,amplifiers, power dividers and other types of components.

In some implementations, the signal delivery system 106 and the quantumprocessor cell 102 are maintained in a controlled QPC environment. TheQPC environment can be provided, for example, by shielding equipment,cryogenic equipment, and other types of environmental control systems.In some examples, the components in the QPC environment operate in acryogenic temperature regime and are subject to very low electromagneticand thermal noise. For example, magnetic shielding can be used to shieldthe system components from stray magnetic fields, optical shielding canbe used to shield the system components from optical noise, thermalshielding and cryogenic equipment can be used to maintain the systemcomponents at controlled temperature, etc. The levels and types of noisethat are tolerated or controlled in the QPC environment can vary, forexample, based on the features and operational requirements of thequantum processor cell 102 and the signal delivery system 106.

In the example quantum processor unit 100 shown in FIG. 1 , the controlsystem 110 controls operation of the quantum processor cell 102. Theexample control system 110 may include data processors, signalgenerators, interface components and other types of systems orsubsystems. In some cases, the control system 110 includes one or moreclassical computers or classical computing components.

FIG. 1 shows an example control system 110A that includes one or moreprocessors 112, memory 114, radio frequency (RF) or microwave (μW)generators 116, radio frequency (RF) or microwave (μW) receivers 118 andDC sources 120. A control system may include additional or differentfeatures and components. In some examples, components of the controlsystem 110A operate in a room temperature regime, an intermediatetemperature regime, or both. For example, the control system 110A can beconfigured to operate at much higher temperatures and be subject to muchhigher levels of noise than are present in the QPC environment.

In some implementations, the control system 110 includes a classicalcomputing cluster, servers, databases, networks, or other types ofclassical computing equipment. For example, the memory 114 can include,for example, a random access memory (RAM), a storage device (e.g., aread-only memory (ROM) or others), a hard disk, or another type ofstorage medium. The memory 114 can include various forms of memory,media and memory devices, including by way of example semiconductormemory devices (e.g., EPROM, EEPROM, flash memory devices, and others),magnetic disks (e.g., internal hard disks, removable disks, and others),magneto optical disks, and CD ROM and DVD-ROM disks. The processors 112may include one or more single- or multi-core microprocessors, one ormore FPGAs or ASICs, one or more other types of data processingapparatus. The processors 112 can generate control information, forexample, based on a quantum program (e.g., a quantum logic circuit, aquantum simulation, a quantum algorithm, etc.) to be performed by thequantum computing system 100 or based on other types of information.

In the example shown, the radio frequency (RF) or microwave (μW)generators 116 and the DC sources 120 can each generate control signalsbased on control information provided by the processors 112. The controlsignals can be delivered to the quantum processor cell 102 by the signaldelivery system 106, for example, and interact with the circuit devices105. In the example shown, the radio frequency (RF) or microwave (μW)receivers 118 can receive and process signals from the quantum processorcell 102. For example, receivers 118 can include a digitizer, amicrowave source, and other types of signal processing components. Thereceivers 118 can process (e.g., digitize, or otherwise process) thesignals from the quantum processor cell 102 and provide the processedinformation to the processors 112. The processors 112 can extract data,for example, to identify the quantum states of qubits in the quantumprocessor cell 102 or for other purposes.

The control system 110A may include multiple domain control subsystems.Each domain control subsystem may include a dedicated processor 112,memory 114, generator 116, receiver 118, DC source 120 and otherresources. In some cases, resources are shared by multiple domaincontrol subsystems. Each domain control subsystem in the control system110A can control an associated domain in the quantum processor cell 102.For instance, a first domain control subsystem controls the first domain101A and a second domain control subsystem controls the second domain101B.

Each domain control subsystem in the example control system 110A cancommunicate with the devices in the associated domain in the quantumprocessor cell 102A. For instance, a generator 116 and DC source 120 inthe first domain control subsystem can send signals to the subset of thecircuit devices 105 in the first domain 101A, and a receiver 118 in thefirst domain control subsystem can receive signals from the subset ofthe circuit devices 105 in the first domain 101A; likewise, a generator116 and DC source 120 in the second domain control subsystem can sendsignals to the subset of the circuit devices 105 in the second domain101B, and a receiver 118 in the second domain control subsystem canreceive signals from the subset of the circuit devices 105 in the seconddomain 101B.

In some instances, the control system 110 generates classical signals,including electrical waveforms or laser fields, which interact withdevices in the quantum processor cell 102 to operate the quantumcomputing system 100; and the control system 110 may also receiveclassical signals back from the devices. To ensure that the classicalsignals are precisely tuned to the relevant device to give the desireddevice behavior and system operation, the control system 110 can becalibrated to the device.

In some instances, the control system 110 implements a calibrationprocess that performs measurements on a quantum computing device andinterprets those measurements to extract control parameters and devicecharacteristics. The device characteristics can be physical attributesof the device, for example, the resonance frequency between the twolowest energy levels of a qubit. Device characteristics can be used todescribe the performance of the device, for example, with respect todesign goals. Control parameters can be parameters of the control system110 that are calibrated to the device, for example, the optimal powersetting for applying a read-out pulse. Correct determination of controlparameters can be important, for example, to enable operation of thequantum computing system 100.

In some aspects of operation, domains of the quantum computing system100 can be identified by operation of the control system 110. Thedomains can include respective domain control subsystems and respectivesubsets of quantum circuit devices 105 in a quantum processor 112 of thequantum computing system 100. In some instances, a first set ofmeasurements can be obtained from a first domain 101A. The first set ofmeasurements can be stored in a memory 114 of the control system 110.Device characteristics of the quantum circuit devices 105 of the firstdomain 101A can be determined by operation of the control system 110based on the first set of measurements. The device characteristics canbe stored in a memory 114 of the control system 110. The control system110 can then determine (i.e., decide or make a determination) to obtaina second set of measurements from the first domain 101A based on thedevice characteristics. The determination to obtain a second set ofmeasurements can be made automatically, for example, based on the devicecharacteristics (and possibly other data) meeting a predefined criterionor set of criteria. For instance, the “example success criteria”described below for various experiments and measurements may be used ascriteria for determining to obtain the second set of measurements. Thesecond set of measurements can be obtained from the first domain 101A.The second set of measurements can be stored in the memory 114 of thecontrol system 110. Quantum logic control parameters for the subset ofquantum circuit devices 105 of the first domain 101A can be determinedby operation of the control system 110A, based on the second set ofmeasurements. The quantum logic control parameters can be stored in adatabase (e.g., a database defined in the memory 114) of the controlsystem 110A for use in operating the first domain. An example of such adatabase is shown and described in connection with FIG. 4 , describedbelow. The control system 110 may perform the same process or a similarprocess for the other domain 101B (e.g., in parallel or otherwise).

In some aspects of operation, the domains 101A, 101B can be defined inpart by hardware, control logic, physical connections, or software inthe quantum computing system 100. The quantum circuit devices 105 of thefirst domain can include qubit devices and readout devices. The controlsystem 110 can include a controller (where the controller includes acache), signal conversion circuitry, a filter, and an amplifier, asfurther shown and described in connection with FIG. 4 . The controlsystem 110 can include an embedded operating system (OS) configured tocommunicate with the database and the controller, as further shown anddescribed in connection with FIG. 4 . The device characteristics caninclude resonance frequencies and coherence times for qubit devices inthe first domain. The quantum logic control parameters can includeread-out pulse parameters or quantum logic gate pulse parameters forqubit devices in the first domain. For instance, the quantum logiccontrol parameters may include the duration, power, frequency, or otherparameters of a π pulse, a π/2 pulse, a two-qubit gate pulse, a readoutpulse, etc. The first set of measurements or the second set ofmeasurements can be repeated based on a success or a failure of acalibration of the first domain of the quantum computing system 100, forexample, as discussed below with respect to FIG. 2 .

FIG. 2 is a block diagram of an example calibration process 200. Theexample calibration process 200 can determine device characteristics andcontrol parameters in a quantum computer system. The calibration process200 will, in general, depend on the design and architecture of thequantum computing system used. The example calibration process 200includes a set of logical blocks, each representing an experimentalmeasurement (e.g. M1-M3), and a procedure to determine the result of themeasurement (e.g. R1-R3). The procedure specifies the measurementsthemselves, and a map from each measurement result to: (a) a newmeasurement (R1, R2); (b) a repetition of the same measurement, possiblywith new parameters (e.g. R2); or (c) a terminal state, indicatingsuccess (R3) or failure of the procedure (R1-R3). On reaching theterminal state, the computer may notify one or more external systems orrecipients (e.g., via email or instant message (e.g. Slack, etc.)).

As shown in FIG. 2 , the first experimental measurement M1 is obtained,and the first measurement result R1 (e.g., a device characteristic of aquantum circuit device) can be determined from the first experimentalmeasurement M1. Based on the first measurement result R1, it can bedetermined to obtain a second experimental measurement M2. For instance,if a device characteristic (e.g., coherence time, qubit frequency,anharmonicity, etc.) determined from the first experimental measurementM1 meets a predefined criterion, then the process 200 may automaticallydetermine to obtain the second experimental measurement M2; but if thedevice characteristic determined from the first experimental measurementM1 does not satisfy the quality criterion, the process 200 mayautomatically determine to move to a terminal state indicating failureF. The second experimental measurement M2 can then be obtained, and thesecond measurement result R2 (e.g., quantum logic control parameters fora quantum circuit device) can be determined from the second experimentalmeasurement M2. For instance, if a quantum logic parameter determinedfrom the second experimental measurement M2 meets a predefinedcriterion, then the process 200 may automatically determine to obtainthe third experimental measurement M3; but otherwise, the process 200may automatically determine to move to a terminal state indicatingfailure F, or to repeat the second experimental measurement M2 (e.g.,using different parameters, etc.). The process 200 can continue in asimilar, automated manner for one or more further experimentalmeasurements (e.g., the third experimental measurement M3) and one ormore further measurement result determinations (e.g., measurement resultR3) until reaching a state representing success S or failure F. Thepredefined criteria used at R1, R2, R3 can include the “example successcriteria” described below or other types of criteria.

The example calibration process 200 is modular in that it may includeseveral sub-procedures. A modular sub-procedure may be reused toimplement a characterization or calibration procedure for differentkinds of devices that share a common component. When the sub-procedureterminates it returns control to the main procedure which uses theresult to determine what to do next. The modular sub-procedures may alsobe used independently of the full experimental procedure. For example, acertain set of control parameters optimal values may drift over time anda sub-procedure to re-calibrate just those parameters that have driftedneed not require a full run of the experimental procedure. This enableson-line calibration, where the operation of the device does not need tobe completely paused in order to recalibrate.

In some cases, there are constraints on measurement ordering, as somemeasurements may only give useful results if particular controlparameters or device characteristics are known to sufficient precision.The experimental procedure can take this into account, for instance, byonly allowing such measurements downstream from the measurement(s) thatdetermine the parameters or characteristics required. Each measurementcan determine one or more device characteristics or control parameters(possibly to finite precision). At the end of each measurement, themeasured characteristics or parameters can be committed to the memory.Thus, as the procedure progresses and eventually terminates, a store ofthe characteristics and parameters is constructed. In someimplementations, all the characteristics and parameters of interest canbe measured and stored.

In some instances, to determine the result of a measurement, the logicalmeasurement block includes a procedure that takes as an input themeasurement data and outputs: (a) extracted values for thecharacteristics and parameters, and (b) a member of the discrete set ofoutputs used to select the next measurement. In (b), the possibilitythat the measurement failed to produce meaningful results can beaccounted for. If the problem is recoverable, like an insufficient scanrange, or additional averaging is necessary, the measurement may berepeated with new parameters. If the error is not recoverable, theexperimental procedure may exit to a failure state. Techniques fordetermining whether the measurement has succeeded or failed may bestatistical in nature, based on some goodness of fit metric for fitteddata (e.g. reduced residual chi-squared statistic, Akaike InformationCriterion, Bayesian Information Criterion, etc.), based on machinelearning, or some combination thereof.

FIG. 3 is a block diagram of an example calibration process 300. Theexample calibration process can be performed in a quantum computingsystem, for example, to characterize and tune up components of thequantum computing system. For instance, the example calibration process300 may be used to calibrate one or more domains, subsystems or devicesin the example quantum computing system 100 shown in FIG. 1 . In somecases, the calibration process 300 is controlled by a control system ofthe quantum computing system. The process 300 may include additional ordifferent operations, and the operations may be performed in the ordershown or in another order. In some cases, multiple operations arecombined, performed in parallel or divided into additional operations.

In some cases, multiple instances of the process 300 are applied inparallel in the respective domains of a quantum computing system. Insome cases, portions of the process 300 may be iterated periodicallyduring operation of the quantum computer system.

At 302, a continuous wave (CW) initialization process is performed. TheCW initialization process may include one or more of the operationsdescribed in the “1. CW Bring-up” section below. In the examplesdescribed, CW measurements are performed over time scales that aresignificantly longer than the coherent lifetimes of the qubits. At 304,a pulsed initialization process is performed. The pulsed initializationprocess may include one or more of the operations described in the “2.Pulse Bring-up” section below. In the examples described, pulsedmeasurements are performed over time scales that are shorter than thecoherent lifetimes of the qubits.

At 306, a single-qubit gate initialization process is performed. Thesingle-qubit gate initialization process may include one or more of theoperations described in the “3. Gate Tune-up” section below. At 308, amulti-qubit gate initialization process is performed. The multi-qubitgate initialization process may include one or more of the operationsdescribed in the “5. Multi-qubit Gate Tune-Up” section below.

At 310, the quantum computer system is operated. For example, thequantum computer system may execute quantum logic circuits or othertypes of quantum algorithms. At 312, one or more of the domains,subsystems or devices in the quantum computing system is recalibrated.The recalibration may include one or more iterations of the operations(302, 304, 306, 308) applied to the whole quantum computing system or toa specific domain, subsystem or device in the quantum computing system.

FIG. 4 is a block diagram of an example quantum computing system 400. Insome cases, the features and components shown in FIG. 4 may be used toimplement aspects of the example quantum computing system 100 shown inFIG. 1 . In various implementations, an embedded operating system (OS)401 serves as a central controller of the system. The embedded operatingsystem 401 may be a real-time operating system embedded on a chip, forexample, a field-programmable gate array (FPGA). The embedded operatingsystem 401 may be a kernel (for example, a Linux kernel) embedded on achip (for example, the FPGA). The embedded operating system 401 may runon a physical CPU with a low-latency connection to the rest of thehardware system of quantum computing system.

In some implementations, the embedded operating system 401 cancommunicate with various databases, the databases comprisinglarger-latency memory caches. The databases can include a predictionsdatabase 402, a data model database 403, and a constraints database 404.In another implementation, while three separate databases are shown indiagram 400, the databases may be consolidated into one database. Thedatabases can contain information pertaining to quantum system anddevice predictions (for example, via the predictions database 402), themodels for extracting parameters from the data (for example, via thedata model database 403), and the constraints for determining successcriteria for the calibration steps (for example, via the constraintsdatabase 404). The data associated with the databases may be stored, forinstance, on a centralized server. The centralized server can beavailable for asynchronous updates. The data may also be storedon-board, for example, on an FPGA controller. This can allow forlow-latency access which may be needed for a given operation of thequantum system.

In some implementations, the operating system can execute a multitude ofprocesses to calibrate the QPU system, as described variously herein.The processes may be executed in parallel. Each process (for example,process 0 405, process 1 415, and process N, not shown) may utilize astack for operation. Examples of such stacks shown in FIG. 4 includestack 0 406, stack 1 416, or stack N 426, where N is a positive integer.In some implementations, the stacks, for example, stack 0 406 and stack1 416, can include electronics, for example, the electronics labeled ascontroller 0 407 and controller 1 217 in FIG. 4 . Controller 0 407 caninclude a cache M0 408, a digital-to-analog converter (DAC), and ananalog-to-digital converter (ADC) shown as DAC/ADC 0 410 in FIG. 4 , asignal chain comprising a filter and an amplifier shown as FILTER/AMP 0412 in FIG. 4 , and relevant QPU elements, shown as QPU ELEM 0 414 inFIG. 4 . Similarly, the controller 1 417 can include a cache M1418, aDAC and an ADC shown as DAC/ADC 1 420, a signal chain comprising afilter and an amplifier shown as FILTER/AMP 1 422 in FIG. 4 , andrelevant QPU elements, shown as QPU ELEM 1 424 in FIG. 4 . Similarcomponents can be defined for additional controllers N (not shown),which can be part of a stack N 426. In some implementations, the QPUelements (for example, QPU ELEM 0 414 and QPU ELEM 1 424) may includecouplings to other parts of the QPU which may be relevant to theexecution of particular operations.

In the following text, a detailed list of example experiments isdescribed. Each experiment provides an example of the equipment andoperations to perform all or part of an initialization or calibrationprocess. A central server or other processor can dispatch the processesto sub-processing units or domain control subsystems that operate adomain in a quantum processor cell. In each experiment, the qubits andtheir measured properties, whose design parameters have been journaled,may be compared and evaluated. The step-by-step process coupled with thecomputing architecture may allow for the tune-up of large scalesuperconducting quantum circuit systems.

1. Continuous wave (CW) bring-up

-   -   a. CW cavity spectroscopy        -   i. Instruments can include RF signal generator with            amplitude and frequency control, RF signal receiver.        -   ii. Single tone continuous-wave measurement            -   1. A two-dimensional power and frequency scan is                performed on the resonator drive line. RF reflected off                the resonator is measured. Both the power and the phase                of the reflected field are measured at each point.                Reflection amplitude dips and resonant phase rolls are                noted as likely resonators. Cross-correlation with                designed resonator frequency allows identification of                likely resonators.            -   2. Nonlinear response from the resonator, known as the                Lamb shift, denotes the presence of a nonlinear system                interacting with the resonator. Cavity responses taken                at a higher power above the nonlinear response are                referred to as the high-power branch. Cavity responses                taken at a lower power below the nonlinear response are                referred to as the low-power branch. The measurement                system decides whether a successful qubit is addressable                via this drive line with the existence of this lamb                shift.        -   iii. Example success criteria can include: (A) Fitted            resonator Q and fitted resonant frequency are compared to            design Q and frequency, a conformance window is specified to            denote success. (B) Measured Lamb shift versus predicted            Lamb shift is also compared to design intent, a conformance            window is specified to denote success. Criteria (A) and (B)            may both need to be satisfied.    -   b. CW qubit spectroscopy        -   i. Instruments can include: 2× RF signal generator with            amplitude and frequency control, and a RF signal receiver        -   ii. Two-tone continuous wave measurement            -   1. A single tone on the low power branch of a                resonator-qubit system is reflected off the resonator.                The reflected signal is constantly monitored for both                its reflected power and its reflected phase. A second                tone is swept in both frequency and power along a qubit                drive line. The response of the first tone reflecting                off the cavity will exhibit changes in its reflected                behavior. These changes will occur when systems coupled                to the cavity change the cavity dressed state as they                are resonantly driven. Cross correlating spectrum of the                designed qubit with observed transition frequencies and                transition strengths for constant drive power, the                system assigns energy level transition frequencies of                single or multi-photon transitions in the qubit.        -   iii. CW Qubit T1 and T2 estimation            -   1. Automatic operation: After identification of the                single photon transition from the 0 qubit state to the 1                qubit state, a variation of the above experiment is                performed. Iteratively lowering the qubit drive power                and the resonator probe power, the Lorentzian response                of the qubit is probed at lower and lower powers. The                system fits Lorentzian to the qubit until the signal to                noise reaches a specific cutoff. The lowest achievable                linewidth of the qubit acts as an indication of the                incoherent linewidth of the qubit, indicating the                approximate T1 relaxation time. The measurement system                can determine to mark the qubit as viable for                computation if the T1 is larger than a preset number.            -   2. Semi-Automatic operation: After identification of the                single photon transition from the 0 qubit state to the 1                qubit state, a variation of the above experiment is                performed. An algorithm iteratively suggests lowering                the qubit drive power and the resonator probe power.                Each suggestion can be easily manipulated by the                operator, or the operator can accept the algorithm's                suggested experimental parameters. A measurement is run                with the new experimental parameters. The system fits                Lorentzian to the qubit until the signal to noise                reaches a specific cutoff. The lowest achievable                linewidth of the qubit acts as an indication of the                incoherent linewidth of the qubit, indicating the                approximate T1 relaxation time. The measurement system                can determine to mark the qubit as viable for                computation if the T1 is larger than a preset number.        -   iv. Example success criteria can include: (A) Fitted            transition frequencies for the 0 to 1 energy splitting and            the 0-2 energy splitting are compared to design intent            within a conformance window. (B) Qubit linewidth is compared            to a minimum achievable linewidth metric, achieving a            linewidth less than the minimum passable linewidth denotes a            success. Criteria (A) and (B) may both need to be satisfied.    -   c. CW Josephson parametric amplifier (JPA) single-tone        spectroscopy        -   i. Instruments can include: RF signal generator with            amplitude and frequency control, RF signal receiver,            controllable constant current source to set magnetic flux            through SQUID loop.        -   ii. Single tone continuous wave measurement            -   1. The Josephson parametric amplifier circuit is a                single port device constructed of a low Q resonator with                a tunable SQUID. RF is sent into the JPA with the use of                a microwave circulator. A tunable resonant mode with a                flux dependent resonant frequency is observed in a 2D                plot of applied flux versus tone frequency. The                reflected RF phase (and to a lesser extent the                amplitude) provides a means of distinguishing the                resonant frequency of the tunable mode. Due to the                asymmetry in the Josephson Junctions a large modulation                of frequencies should be accessible, observing a                repetitive pattern indicates a well behaved JPA.        -   iii. Example success criteria can include: (A) A successful            fit, with low chi squared, to the periodic modulation of the            resonant frequency denotes success.    -   d. CW JPA gain optimization        -   i. Instruments can include: a 2× RF signal generator with            amplitude and frequency control, RF signal receiver, tunable            constant current source to set magnetic flux through SQUID            loop.        -   ii. Two-tone continuous wave measurement            -   1. Both a pump RF tone and a signal tone are sent into                the JPA via a microwave circulator. Using a directed                search algorithm, the pump tone's frequency and power                are scanned by the automated search algorithm along with                the applied flux to the JPA. The signal tone's frequency                is chosen to be the frequency we are interested in                amplifying. The signal tone is measured both with and                without the pump tone present multiple times.                Amplification and noise in the repeated measurements are                measured. The amplification divided by the noise in the                amplification are sent to the directed search algorithm                to maximize their ratio for a given pump frequency,                power and applied flux.        -   iii. Example Success Criteria can include: (A) The amount of            gain achieved is compared to the design specification for            minimum gain, success denotes measuring more gain than the            minimum required.            2. Pulse bring-up    -   a. Cavity spectroscopy        -   i. Instruments can include: pulsed RF signal generator with            amplitude and frequency control, Pulsed RF signal receiver        -   ii. 2D cavity spectroscopy            -   1. A measurement is performed with pulses longer than                the cavity ring-up time. Varying the power of the RF                pulse and the frequency of the pulse a two dimensional                scan is taken. Fitting the reflected power or frequency                response of the demodulated reflected pulses a lamb                shift measurement is observed. Pattern recognition                algorithms discover the low power branch and identify                possible pulse parameters to save as a candidate readout                point, including the frequency and power of the pulse                for an on-resonant low power interrogation of the                readout resonator.        -   iii. Example success criteria can include: (A) Successful 1D            fits of cavity response versus frequency denote success. (B)            Producing a candidate readout point also denotes success.            Criteria (A) and (B) may both need to be satisfied.    -   b. Rabi spectroscopy of the qubit        -   i. Instruments can include: 2× pulsed RF signal generator            with amplitude and frequency control, and a pulsed RF signal            receiver.        -   ii. Pulsed measurement involving a qubit drive pulse and a            cavity interrogation            -   1. Using the frequency discovered by 1.b.iii. CW Qubit                T1/T2 estimation, qubit pulses much shorter than the                coherent lifetime of the qubit are sent at varying                frequencies to the qubit drive line. Subsequent                interrogation of the cavity is recorded for each pulse                that is sent. The response of the cavity resonator will                trace out a coherent Rabi line shape of the qubit.            -   2. Or Using the frequency discovered by 1.b.iii. CW                Qubit T1/T2 estimation, qubit pulses much longer than                the coherent lifetime of the qubit are sent to the qubit                drive line. Subsequent interrogation of the cavity is                recorded for each pulse that is sent. The response of                the cavity resonator will trace out an incoherent                Lorentzian at the qubit frequency.        -   iii. Example success criteria can include: (A) Successful            fit to qubit resonance, either a driven Rabi lineshape (1)            or a Lorentzian lineshape (2) can denote success.    -   c. Power Rabi        -   i. Instruments can include 2× pulsed RF signal generator            with amplitude and frequency control, and pulsed RF signal            receiver        -   ii. Pulsed measurement involving a qubit drive pulse and a            cavity interrogation            -   1. Given a successful frequency measurement and response                from measurement 2.b. A fixed-time interval pulse is                sent to the qubit drive line. Followed by a subsequent                cavity interrogation. The amount of RF power is varied                from 0 to a maximum achievable from the RF                instrumentation. At each RF power the cavity's response                will mirror the state of the qubit. Oscillations are fit                to a simple power-broadened Rabi flopping model, where a                sinusoid with qubit-drive, amplitude-dependent frequency                is observed.                -   a. Advanced readout calibration is also accomplished                    by defining the axis in I/Q space with the largest                    variance from the measurement. This defines the                    optimal quadrature. All subsequent measurements can                    be projected onto the saved optimal quadrature.        -   iii. Success criteria can include: (A) Successful fit to a            power Rabi curve denotes success. (B) Amplitude to Rabi            Frequency conversion is compared to design intent, agreement            to conformance window denotes success. Criteria (A) and (B)            may both need to be satisfied.    -   d. Ramsey spectroscopy        -   i. Instruments can include: 2× pulsed RF signal generator            with amplitude and frequency control, and pulsed RF signal            receiver        -   ii. Pulsed measurement involving two separated qubit drive            pulses and a cavity interrogation            -   1. A π/2 pulse is sent down the qubit drive line, after                a variable duration of no RF pulse another π/2 pulse is                sent down the qubit drive line, followed by a cavity                interrogation pulse. By varying the delay time and                plotting the cavity response as a function of delay time                a Ramsey spectrum can be observed.                -   a. Additionally, the second π pulse can be given a                    phase offset. This phase offset mimics the local                    oscillator of the qubit drive as having been detuned                    during the variable duration wait time. Subsequently                    the Ramsey spectrum will have a clear frequency                    offset which allows for easier data fitting between                    the timescales of the Ramsey oscillation and the                    decay of the coherence of the qubit.                -   b. Both measurements allow for carefully fitting the                    qubit resonance.        -   iii. Example Success Criteria can include: (A) Successful            fit to a Ramsey curve denotes success. (B) Detuning fit            parameter must not exceed expected detuning parameter beyond            a conformance window. Criteria (A) and (B) may both need to            be satisfied.    -   e. Power Rabi        -   i. Measurement 2.c.i. Is repeated with the newer more            accurate qubit frequency/detuning.        -   ii. Example success criteria can include: (A) Successful fit            to a Power Rabi curve denotes success. (B) Amplitude to Rabi            Frequency conversion is compared to design intent, agreement            to conformance window denotes success. Criteria (A) and (B)            may both need to be satisfied.    -   f. T1        -   i. Instruments can include: 2× Pulsed RF signal generator            with amplitude and frequency control, and pulsed RF signal            receiver.        -   ii. Pulsed measurement involving one qubit drive pulse, a            variable delay, and a cavity interrogation.            -   1. Using the pulse parameters from 2.d. and 2.e. The                state of the qubit is inverted via a π pulse. A variable                delay where no RF is performed on the qubit of interest.                After each delay a cavity interrogation tone is sent to                probe the cavity's response and map the state of the                qubit. Repeating the experiment many times the                relaxation time to the qubit ground state is measured.                -   a. Delay times are made from logarithmically spaced                    samples to probe very large ranges of possible delay                    times.        -   iii. Example Success Criteria can include: (A) successful            fit to a decay curve denotes success. (B) The decay constant            must be sampled at a sufficiently long timescale,            measurements are repeated increasing the sampling time in a            fixed manner until the sampling time and the decay constant            meet an explicit ratio to within a conformance window.            Criteria (A) and (B) may both need to be satisfied.    -   g. T2 taken with Ramsey Spectroscopy        -   i. Instruments can include: 2× Pulsed RF signal generator            with amplitude, frequency, and phase control, and a pulsed            RF signal receiver.        -   ii. Pulsed measurement involving two separated qubit drive            pulses and a cavity interrogation            -   1. A π/2 pulse is sent down the qubit drive line, after                a variable duration of no RF pulse another π/2 pulse is                sent down the qubit drive line, followed by a cavity                interrogation pulse. By varying the delay time and                plotting the cavity response as a function of delay time                a Ramsey spectrum can be observed.                -   a. Additionally, the second π pulse can be given a                    phase offset. This phase offset mimics the local                    oscillator of the qubit drive as having been detuned                    during the variable duration wait time. Subsequently                    the Ramsey spectrum will have a clear frequency                    offset which allows for easier data fitting between                    the timescales of the Ramsey oscillation and the                    decay of the coherence of the qubit. Performing the                    measurement such that the frequency offset                    oscillations and the T2* act on sufficiently                    separated (>5×) timescales allows for good fitting                    of the data and accurate extraction of the T2* time.        -   iii. Example success criteria can include: (A) Successful            fit to a Ramsey curve denotes success. (B) The Ramsey curve            decay constant must be sampled at a sufficiently long            timescale, measurements are repeated increasing the sampling            time in a fixed manner until the sampling time and the decay            constant meet an explicit ratio to within a conformance            window. Criteria (A) and (B) may both need to be satisfied.            3. Gate tune-up    -   a. Readout optimization        -   i. Instruments can include a 2× Pulsed RF signal generator            with amplitude and frequency control, and a pulsed RF signal            receiver.        -   ii. Pulsed measurement to optimize the readout fidelity            -   1. For subsequent measurements cavity interrogation                parameters need to be more precisely set. Repeatedly                inverting the qubit population via a π pulse on the                qubit drive line followed by a cavity interrogation                supplies a histogram of cavity responses. Performing the                same measurement without the qubit inversion provides                cavity responses for the qubit in the ground state.                Training a binary classifier on the separation of these                two data sets with normal ROC curve metrics provides                objective functions that can be optimized by changing                the cavity interrogation parameters. Feeding these                objectives into an automatic system that repeats the                measurements to maximize the achievable assignment                fidelity by optimizing the cavity interrogation time,                frequency, and power allows the system to tune itself to                optimal readout conditions.                -   a. Optimal quadrature settings are updated with the                    further refined cavity interrogation parameters.        -   iii. Example Success Criteria can include: (A) Measured            readout fidelity may need to meet or exceed design            specification.    -   b. AC Stark coefficient measurement        -   i. Instruments can include: 2× pulsed RF signal generator            with amplitude, frequency, and phase control, pulsed RF            signal receiver        -   ii. Pulsed measurement to optimize drive detuning            -   1. Qubit driving fields are detuned from multiple                different transitions. Detuned driving of these                resonances causes dispersive shifts on these levels                leading to a power dependent shift of the ground to                first excited state of the qubit. Scanning the amplitude                of a power dependent tuning coefficient repeated pulse                sequences bringing the qubit partially toward its                excited state and then back to the ground state are sent                to the qubit along the qubit drive line followed by a                cavity interrogation. For longer and longer sequences of                repeated pulses the error associated with detuning can                be amplified. The AC stark coefficient is found to be                optimal when the qubit returns to its ground state. This                value is saved, and subsequent pulses are modulated by                this coefficient.        -   iii. Example success criteria can include (A) Measured AC            stark coefficient must conform to design window            specifications. (B) Fidelity of returning to ground state            may need to be greater than predefined success criteria.            Criteria (A) and (B) may both need to be satisfied.    -   c. π-π Amplitude tune-up        -   i. Instruments can include: a 2× Pulsed RF signal generator            with amplitude, frequency, and phase control, Pulsed RF            signal receiver.        -   ii. Pulsed measurement to optimize over and under rotation            errors            -   1. To optimize the effect of gates on the qubit,                repeated applications of the same gate are performed on                the qubit. Errors in the parameters of the gate will                cause over (or under) rotation of the qubit state. By                performing sequences that should nominally return the                qubit to its initial state, any deviation from idealized                pulses will cause there to be a different qubit state                measured.                -   a. The qubit is first rotated by a π/2 pulse to be                    in a superposition of the ground and excited state,                    placing the state of the qubit on or near the                    equator of the Bloch sphere. An even number of                    subsequent π/2 pulses (0, 2, 4, 6, etc.) are then                    sent to the qubit. For an optimal pulse this will                    rotate the qubit to the equator again. Subsequent                    cavity interrogations will reflect the state of the                    qubit. Any deviation of the qubit state (as measured                    by the cavity) from its original position on the                    Bloch sphere will be indicative of an under or over                    rotation. An optimization algorithm automatically                    adjusts the amplitude of the pulse to correct for                    over/under rotation errors by probing larger numbers                    of applied pulses, such that small errors are                    amplified.                -   b. The qubit is first rotated by a π/2 pulse to be                    in a superposition of the ground and excited state,                    placing the state of the qubit on or near the                    equator of the Bloch sphere. Any number of                    subsequent π pulses (0, 1, 2, 3, etc.) are then sent                    to the qubit. For an optimal pulse this will rotate                    the qubit to the equator again. Subsequent cavity                    interrogations will reflect the state of the qubit.                    Any deviation of the qubit state (as measured by the                    cavity) from its original position on the Bloch                    sphere will be indicative of an under or over                    rotation. An optimization algorithm automatically                    adjusts the amplitude of the pulse to correct for                    over/under rotation errors by probing larger numbers                    of applied pulses, such that small errors are                    amplified.        -   iii. Example success criteria can include: (A) A fractional            deviation from the equator is calculated and an inferred            over/under rotation error is calculated, this is compared to            a passing criterion associated with the number of pulses            performed.    -   d. DRAG tune-up        -   i. Instruments can include: 2× Pulsed RF signal generator            with amplitude, frequency, and phase control, and Pulsed RF            signal receiver.        -   ii. Pulsed measurement to optimize leakage error from            driving the qubit to its second excited state.            -   1. So-called leakage errors occur when power-broadening                of the qubit linewidth starts to show significant                coherent drive to the second excited state of the qubit.                Reducing this can be accomplished by applying a                derivative of the pulse envelope to the opposite RF                driving quadrature. The amplitude of this opposite                quadrature drive signal can be scaled by a unitless                coefficient. Optimally setting this coefficient to                maximally reduce leakage will reduce gate infidelity.                Different sequences of pulses that are especially                sensitive to detuning errors when driving the qubit,                like mixtures of π/2 pulses about X and π/2 pulses about                Y will exhibit opposite signed errors. By playing                repeated sequences of X/2 and Y/2 pulses the error can                be amplified. Sending repeated X/2, Y/2 sequences along                the qubit drive line followed by a cavity interrogation                pulse allows us to map the position of the qubit on the                Bloch sphere. Repeating the experiment but permuting the                order of the π/2 pulses (to Y/2, X/2) can cause residual                error to accumulate in the opposite direction along the                Bloch sphere. The difference between these two signals                is fed into an optimizer that changes the DRAG amplitude                coefficient. The optimizer works to minimize the                difference between these two measurements and saves the                DRAG amplitude coefficient such that all pulses know                include the DRAG correction.        -   iii. Example success criteria can include: (A) The goodness            of fit for the fitted crossing of the two measurements is            compared to a minimum goodness of fit. (B) The fitted DRAG            coefficient must fall within a specified window to denote            success. Criteria (A) and (B) may both need to be satisfied.    -   e. π-π Fine-tune        -   i. Instruments can include: 2× Pulsed RF signal generator            with amplitude, frequency, and phase control, and a pulsed            RF signal receiver.        -   ii. Pulsed measurement to optimize over and under rotation            errors            -   1. A repetition of measurement 3.c is performed after                the inclusion of DRAG.        -   iii. Example success criteria can include: (A) A fractional            deviation from the equator is calculated and an inferred            over/under rotation error is calculated, this is compared to            a passing criterion associated with the number of pulses            performed.    -   f. Perform randomized benchmarking        -   i. Instruments can include: 2× Pulsed RF signal generator            with amplitude, frequency, and phase control, and a Pulsed            RF signal receiver        -   ii. Pulsed measurement to verify functionality of tuned            gates            -   1. For a given circuit length a random quantum circuit                is constructed by choosing elements from the Clifford                algebra group, including the last elements which                effectively invert the operation of all previous                elements on the qubit. This procedure is repeated                multiple times. For each random circuit the pulses are                sent to the qubit followed by a cavity interrogation and                the result is saved. Gate errors and state preparation                and measurement errors will lead to the qubit not being                measured in the ground state. This experiment is                repeated for multiple random circuits and for multiple                lengths of random circuits. Gate fidelity is inferred by                fitting the averaged results of all these measurements                by a power-law function as at low fidelities or at long                times the constant application of gates will drive the                qubit to the equator of the Bloch sphere.        -   iii. Example success criteria can include: (A) A minimum            achieved gate fidelity must be fit to denote success.    -   g. Perform further benchmarking algorithms        -   i. Instruments can include: 2× Pulsed RF signal generator            with amplitude, frequency, and phase control, and a pulsed            RF signal receiver        -   ii. Perform Gate Set Tomography            -   1. To verify the gate unitaries and the measurement                accuracy Gate Set Tomography is performed.        -   iii. Example success criteria can include: (A) A minimum            achieved gate fidelity must be fit to denote success.            4. Tunable qubit bring-up (automated bring-up variation for            flux-tunable qubits)    -   a. Instruments can include: a 2× Pulsed RF signal generator with        amplitude, frequency, and phase control, Pulsed RF signal        receiver, tunable constant current source to set magnetic flux        through SQUID loop.    -   b. In a loop over flux bias values bring up qubit similar to (2)        above:        -   Before beginning a loop of bring-ups for different flux            settings, follow the normal bring-up procedure (2) for a            starting flux value.            -   Strategy I: Terminate after 1 flux period, adjust step                size to achieve fixed delta in qubit frequency.            -   Strategy II: Specify a sequence of flux bias values.            -   Following either strategy I or II.        -   i. Set constant current source to new constant flux bias            current, changing it at a controlled rate.        -   ii. Choose readout settings            -   1. For dispersive readout, perform measurement 2.a.i.,                set readout frequency to be on resonance with cavity                resonance.            -   2. For high-power (nonlinear) readout, use previously                saved readout settings.        -   iii. Perform qubit spectroscopy as specified in (2.c) and            project IQ data onto most recently measured optimal readout            axis.        -   iv. Perform power Rabi measurement as in 2.c.        -   v. Optimize readout as in (3.a) and update the readout            settings (frequency, power, pulse width, or any set of            parameters of the readout pulse and readout acquisition            system).        -   vi. Measure T1 as in 2.f.            -   1. Guess the T1 value to be measured.                -   a. In the first iteration of the loop this is                    brought in from a previous instance of (2.f) at a                    nearby (or the same) flux bias.                -   b. For subsequent guesses, extrapolate from previous                    guesses.                -    i. Due to noise (including non-Markovian noise) in                    the T1 measurements, digital filtering is employed                    to smooth the data.                -    1. Exponentially weighted averaging to extrapolate                    future iterations is employed.        -   vii. Measure T2* as in 2.g. (Ramsey)            -   1. Guess the T2 value to be measured.                -   a. We follow the same strategy as in (4.b.vi.1), for                    the same reasons (noise in T2* values).        -   viii. Measure T2 and CPMG            -   1. Pulsed measurement for extracting T2 and noise                sensitivity of qubit.                -   a. Performing a Ramsey T2* experiment as in 2.g but                    with the inclusion of π (echo) pulses the qubit's                    response to different numbers of echo pulses can be                    mapped out. Measurements are performed where the                    delay time is evenly divided by the number of echo                    pulses performed on the qubit.    -   c. Fit the qubit frequency versus flux bias data to a model and        extract Hamiltonian parameters with uncertainties.    -   d. Generate the pure dephasing rate (1/T2−½T1) and the gradient        of the transition frequency f01 and fit the data to a linear        equation and extract the flux noise amplitude and the background        noise level.    -   e. At a flux insensitive point (f_(min) or f_(max)):        -   i. Perform gate tune-up as in (3) above.        -   ii. Perform benchmarking as in (3.g.) above.            5. Multi-qubit gate tune-up    -   a. Instruments can include 4× Pulsed RF signal generator with        amplitude, frequency, and phase control, 2× Pulsed RF signal        receiver    -   b. Measure qubit-qubit coupling        -   i. Fixed coupling designs            -   1. π—Ramsey measurement                -   a. After both qubits have been individually tuned                    for Single qubit operation a variation on the Ramsey                    experiment (2.d) is performed. On one qubit,                    designated as qubit A, a Ramsey experiment (2.d.) is                    performed. Immediately preceding this measurement on                    the other qubit, designated as qubit B, a π pulse is                    sent exciting qubit B to its first excited state. A                    Ramsey curve is fit to qubit A's resonator response.                    The difference between the fitted detuning and the                    expected detuning is denoted as the qubit A−qubit B                    chi.            -   2. Example success criteria can include: (A) The fitted                chi is compared to the designed chi.        -   ii. Tunable qubit designs            -   1. For weak coupling, π-Ramsey measurement                -   a. At a given constant current flux bias measurement                    5.b.i.1.a is performed.            -   2. For strong coupling, avoided crossing Rabi                spectroscopy                -   a. A tunable qubit, designated qubit A, is tuned                    into resonance with another qubit, designated                    qubit B. Similar to 2.b, a Rabi spectroscopy curve                    is taken. Because both qubits have hybridized one                    will measure two response peaks. This spectrum is                    fit and the splitting between the peaks is related                    to the qubitA−qubit B coupling.            -   3. Example success criteria can include: (A) The fitted                chi or qubit-qubit resonance coupling g is compared to                the design intent.    -   c. Implement gates        -   i. Fixed coupling designs            -   1. Two qubit Ramsey oscillations                -   a. For fixed frequency designs the inherent ZZ                    coupling allows a phase accumulation to occur which                    when pre-pended and post pended with single qubit                    gates creates a CNOT-like gate. By performing the                    single qubit gates and varying the time delay the                    gate's action on both qubits can be characterized.                    Further optimization utilizing INEPT pulse sequences                    can be used to enhance the insensitivity to exact                    tuning of the delay time.            -   2. Example success criteria can include: (A) Delay times                measured during a Ramsey tune-up are compared to                calculated wait times, agreement to within a specified                window denotes success.        -   ii. Tunable qubit designs            -   1. Fast actuation                -   a. Similar to the above measurement of 5.c.i.1.a the                    gate is implemented by allowing the two qubits to                    interact for a specified amount of time. However,                    with a tunable qubit one can significantly change                    interaction between qubitA, the tunable qubit, and                    qubit B, the other qubit. A π pulse is first sent to                    qubit A putting it into its excited state.                    Subsequently, a fast DC pulse is sent to the flux                    port of qubit A, this approximately square pulse                    tunes the qubit between a parking flux and an                    interaction flux. By varying the interaction flux                    and the interaction time the states of both qubitA                    and qubit B can be measured. For fixed interaction                    flux set points resonant swapping of which qubit is                    excited in a Rabi flopping manner. The frequency of                    these Rabi Flops can be maximized exactly when the                    interaction flux point brings qubit A into resonance                    with qubit B.            -   2. Example success criteria can include: (A) Successive                Rabi flopping curves may need to show good fit to the                state of each qubit versus the interaction time. (B) A                maximum swapping Rabi frequency must occur. Criteria (A)                and (B) may need to be both be satisfied.                6. Multi qubit benchmarking    -   a. Variations of randomized benchmarking        -   i. Similar to 3.f. a randomized benchmarking can be            performed which intersperse two qubit swap gates throughout            a randomized benchmarking sequence. Constructing a two qubit            randomized benchmarking sequence is then a matter of            following the excitation sequence, but assigning gates to            different qubits based on the position of the randomized two            qubit swaps. By bounding how often swaps can occur, an idle            qubit can have short sequences of single qubit randomized            benchmarking which returns the idle qubits back to their            ground state in time to meet their randomly scheduled swaps.        -   ii. Example success criteria can include: (A) A decay curve            is fit to a single qubit gate fidelity number this number is            compared to a fixed minimum achievable fidelity. (B) This            experiment is repeated with different numbers of two qubit            swaps used, the lower fidelity puts a bound on the two qubit            gate fidelity. Criteria (A) and (B) may need to be both be            satisfied.    -   b. Optimized gates set tomography        -   i. Similar to 3.g.ii Gate set tomography is taken with a            reduced gate set.        -   ii. Example success criteria can include: (A) A minimum            fidelity for each gate may need to be met.

In the following text, additional example experiments are described.Each experiment provides an example of operations to perform all or partof an initialization or calibration process. A central server or otherprocessor can dispatch the processes to sub-processing units or domaincontrol subsystems that operate a domain in a quantum processor cell. Ineach experiment, the qubits and their measured properties, whose designparameters have been journaled, may be compared and evaluated. Thestep-by-step process coupled with the computing architecture may allowfor the tune-up of large scale superconducting quantum circuit systems.

Some implementations of a two-qubit entangling gate using an alternatingfixed-tunable architecture involves adiabatically tuning a flux-tunabletransmon such that the two-qubit |1,1> state approaches resonance withthe |0,2> state. In this notation, |f,t> indexes the fixed (f) andtunable (t) qubits. Examples of two-qubit entangling gates using afixed-frequency qubit device and a tunable-frequency qubit device aredescribed in the publication “Parametrically Activated Entangling GatesUsing Transmon Qubits” by S. Caldwell, et al., arXiv:1706.06562[quant-ph], Jun. 20, 2017. In some implementations, an automated processis used for discovering the parameters for such entangling gates. Inparticular, such parameters can include quantum logic controlparameters; as an example, the quantum logic control parameters caninclude a parameter for a flux pulse configured to implement acontrolled-phase (CPHASE) interaction.

In order to find the operating point for a given interaction (forexample, a controlled-phase interaction) the follow may need to bedetermined: (1) the parking point for the tunable qubit, (2) the fastflux pulse amplitude required to throw the qubit to a given interactionlocation, (3) the fast flux pulse duration that results in a π phaseaccumulation on the |11> state, and (4) the phases accumulated by the101> and 110> states during the interaction. The term “zeta” can bereferenced herein to refer to the rate of entangling phase accumulationin the CPHASE interaction, e.g., the rate at which the |11> stateacquires a phase that may not be acquired by states |01> or |10>. Insome cases, a calibration process includes one or more of the followingsteps performed in the following order or in another order:

-   (1) For the determination of the parking point, flux bias automation    can be used to measure the frequency versus flux bias of the tunable    qubit. The bias point can be chosen giving the tunable parking    frequency, such as the maximum or minimum of the frequency curve.-   (2) For the determination of the flux pulse amplitude, the follow    can be performed.    -   (a) The zeta versus flux bias data can be taken from flux bias        automation to estimate the desired frequency for the tunable        qubit during the gate.    -   (b) A measurement such as a flux-time Ramsey measurement can be        used to measure the tunable qubit frequency as a function of        flux pulse amplitude.    -   (c) Step (b) can be repeated for several values of amplitude to        sample the frequency versus the amplitude, as shown in FIG. 5 .    -   (d) This data can be interpolated to identify the amplitude        giving the desired frequency.    -   (e) The desired zeta can be verified by performing a zeta        measurement (for example, by measuring the frequency of the        tunable qubit with the neighbor in both 0 and 1 states, as the        zeta is the difference of the two frequencies). If necessary,        the pulse amplitude can be fine-tuned to obtain the desired        zeta.-   (3) For the determination of the flux pulse duration, the following    can be performed.    -   (a) The desired phase can be used to estimate the corresponding        gate time using the formula: (desired phase)=zeta*(duration).    -   (b) For times near the estimated duration, steps 1-3 in FIG. 6        (described below) can be followed.-   (4) For the |01> and the |10> phases, step 4 in FIG. 6 (described    below) can be followed. Accordingly, the information for the CPHASE    can be known for the desired phase angle.

In some implementations, the above technique can be adapted to otherphysical implementations of CPHASE interactions, beside the use of aflux pulse on a tunable qubit. Such additional implementations caninclude considerations of how the underlying zeta depends on theimplementation. For example, phase tomography, which can be used to findthe |01> and |10> phases, can also be extended to another CPHASE gatediscovery procedure.

FIG. 5 shows a plot 500 of the qubit frequency in units of megahertz onthe y-axis 502 versus the flux pulse amplitude in units of millivolts onthe x-axis 504. For the example plot 500, the flux pulse amplitude canrange from approximately 320 millivolts to approximately 390 millivolts,and the qubit frequency can range from approximately 3680 megahertz toapproximately 3840 megahertz. For the example plot 500, the line 508characterized by y=2.169*x+2997.631 can be used to fit the points of theplot 500.

FIG. 6 shows a diagram 600 representing example CZ gate tune-upprocesses 601 and 603. In some implementations, the processes can usephase tomography to obtain phases for qubits. The x-axis can representphase, and the y-axis can represent amplitude. In particular, process601 can include a +X/2 phase 602, a +F variable duration r phase 604, a+X/2 phase 606, and a readout (RO) phase 608. Further, process 603 caninclude a +X/2 phase 612, a +F variable duration τ phase 614, a +Y/2phase 616, and a RO phase 618.

In a first step, phase tomography on fixed transmons can be performed.Accordingly, the phase tomography on fixed transmons can be tunable inthe zero state. This can allow for the determination of ϕ₁₀(τ).

In a second step, phase tomography on fixed transmons can be performed.Accordingly, the phase tomography on fixed transmons can be tunable inthe one state. This can allow for the determination of ϕ₁₀(τ)+ϕ_(CZ)(τ).

In third step, a subtraction of the phases determined above can beperformed. Accordingly, τ* can be determined, where ϕ_(CZ)(τ*)=π. Thiscan allow for the additional determination of ϕ₁₀(τ), where τ* is the CZpulse duration.

In a fourth step, phase tomography on tunable transmons can beperformed. Accordingly, ϕ₀₁(τ) can be obtained and ϕ₀₁(τ*) can bedetermined. In some implementations, the CZ gate can thereby beobtained. Thus, the amplitude and duration, ϕ₁₀, ϕ₀₁, and ϕ_(CZ) for theCZ can be thereby obtained.

In some implementations, flux bias automation is used for tunable qubitbring-up. In one implementation, the flux bias automation can includethe calibration and characterization of a tunable qubit as a function ofa (1) slow (for example, direct current) flux bias, that is, a flux biasvoltage or current that is held constant during a set of measurements,or (2) measurements of tunable qubits as a function of fast fluxamplitude and fast flux modulation frequency.

In some implementations, flux bias automation (FBA) can refer to a setof measurements that are performed in a specific sequence within a loopover DC flux bias values, with a specific data flow, as shown in FIG. 7(described in further detail below). In particular, FIG. 7 shows adiagram 700 of a process for flux bias automation. In someimplementations, domains can be updated, where the domains can includeat least one flux-tunable qubit device; further, sets of measurementscan be obtained by performing a measurement sequence within a loop overmultiple flux bias values for the flux-tunable qubit device.

In some implementations, when the flux bias is changed, a subset ofmeasurements is performed which can be referred to as repark flux biasand can include (reference to various elements in FIG. 7 are madeherein):

-   -   1) Updating the readout point        -   a) A low-power readout can be updated by performing            low-power cavity spectroscopy 716 and updating the readout            frequency to a given point relative to the cavity peaks with            the qubit in the 0 or 1 state.        -   b) A high-power readout can be updated by performing a            cavity power scan at the high-power cavity frequency with            both 0 and 1 qubit preparations, and by determining the            power at which the difference of the two transmission            measurements is maximized.        -   c) The updated readout power or frequency can be saved to            the database 712.    -   2) Updating the qubit frequencies        -   a) Qubit spectroscopy or Ramsey frequency measurement 718            can be performed to obtain the qubit frequency at the new            flux bias.        -   b) The qubit frequency at the new flux bias can be saved to            the database 712.        -   c) The qubit f₀₂/2 can be measured using high-power qubit            spectroscopy.        -   d) The qubit frequency with any neighboring qubits of            interest (for example, for use in two-qubit gates) prepared            in their 1 states can be measured.        -   e) These frequencies or their differences (for example,            qubit-qubit dispersive coupling, e.g., zeta's) from the            frequency found in (a), can be saved to the database,            indexed by the neighbor id.    -   3) Updating the readout optimal quadrature        -   a) A power Rabi measurement 720 can be performed and the            optimal readout quadrature can be identified. In one            implementation, the principal component of the in-phase and            quadrature (IQ) data to find the axis in the IQ plane along            which the sensitivity of the readout to the qubit state is            maximized.) This axis can then be updated.        -   b) The updated optimal quadrature data can be saved to the            database 712.            In some implementations, model and bootstrapping technique            for choosing how to automatically construct the qubit            frequency measurements is described below. In FBA, the            relaxation and coherence times can be measured. With updated            readout and gate parameters, the coherence properties of the            qubit can be characterized as follows.    -   1) T1 can be measured 722 and stored in the database 712.    -   2) T2* can be measured (for example, using Ramsey technique 724)        and can be stored in the database 712.    -   3) T2 echo (for example, including an extra π pulse during a        Ramsey wait) can be measured and stored in the database.    -   4) Step (3) can be repeated for additional n-π pulses. This can        be implemented as a Car-Purcell-Meiboom-Gill (CPMG) experiment.        The decay time for the n π-pulses can be stored in the database        712.

In some implementations, the T2 measurements are constructed such thatthe fitting returns valid results. In some implementations, this processcan provide optimizing gates and performing benchmarking. In some cases,the gates can be optimized, and benchmarking can be performed using oneor more of the following steps in the order described or in anotherorder:

-   -   1) An automated 1-qubit gate tune-up can be performed.    -   2) A 1-qubit randomized benchmarking process can be performed.    -   3) A 1-qubit gate set tomography can be performed.        -   a) Other automated fine-tuning and benchmarking processes            can be performed, including, for example, Josephson            parametric amplifier (JPA) optimization.        -   b) Readout point fine-tuning can be performed.            As the DC flux bias of the target is changed, the measured            parameters can be stored in a flux dependence table in the            database. This can allow for the improvement of            interpolation and/or extrapolation, and initial parameter            guessing procedures.    -   (1) To determine the flux bias value that coarsely corresponds        to one flux quantum, a cavity spectroscopy can be performed as a        function of slow flux bias. This can be used in connection with        the spectrum model for extrapolation, as its flux bias value may        be sensitive to the initial value of flux bias period.    -   (2) After measuring transition frequency f₀₁ (f₁₂) values, the        estimated flux bias period can be used to fit the f₀₁ (f₁₂)        spectrum model. The estimated flux bias period can then be        extrapolated by evaluating the model at the subsequent slow flux        or fast flux value.        In some implementations, additional measurements can be included        in the flux bias automation, for example:    -   (1) Single-qubit gate optimization at slow flux bias points.    -   (2) Single-qubit randomized benchmarking at slow flux bias        points.        In some implementations, retrying schemes can be implemented for        many of the measurements in the flux bias automation, for        example:    -   (1) Ramsey measurements can determine success criteria based on        the standard error of the mean of the parameters estimated by        one or more fitting models. If the standard error falls outside        of acceptable tolerance ranges, the Ramsey experiment can be        performed again with a larger detuning, smaller span, and        smaller step size.        In addition to measurements as a function of slow flux, tunable        qubits can be characterized as a function of fast flux amplitude        (with fixed slow flux) and as a function of flux modulation        frequency (with fixed slow flux and fast flux amplitude). This        allows determination of the following:    -   (1) Fast flux pulse throw as a function of flux pulse amplitude.    -   (2) Qubit-qubit dispersive coupling (zetas) as a function of        flux pulse amplitude.    -   (3) Coherence times during fast flux and parametric flux pulse.    -   (4) Modulation detuning as a function of flux pulse amplitude        and frequency.        In addition to fitting the qubit f₀₁ spectrum model, the data        collected by these automation procedures can be used to extract        other design parameters:    -   (1) Resonator frequency vs. slow flux bias.    -   (2) Effective qubit frequency vs fast flux amplitude at fixed        modulation frequency.    -   (3) A direct current crosstalk matrix.    -   (4) A qubit-qubit dispersive coupling (zeta) matrix.    -   (5) A flux noise model.    -   (6) Anharmonicity vs slow flux bias.        For chips with multiple tunable qubits, current on one flux bias        line can change the frequencies of other qubits on the same        chip, which can be characterized by a DC crosstalk matrix. One        or more of the following steps may be performed in the following        order or in another order:    -   1) A flux-bias point of high sensitivity can be chosen to        incremental flux bias for the tunable qubits.    -   2) The flux bias on the flux bias lines can be incremented. For        each increment the qubit frequency of the (tunable) qubits on        the chip can be measured.    -   3) A two-dimensional matrix (in units of        delta-frequency/delta-flux) can be obtained.    -   4) Using the known frequency curve of each qubit (known from        FBA), this matrix can be converted to units of delta-bias (qubit        1)/delta-bias (qubit 2), which can be dimensionless and constant        across biases.    -   5) This matrix can be stored in a database.        In some implementations, the frequency measurements are        bootstrapped, for example, using one or more of the following        steps in the following order or in another order:    -   1) Starting at zero flux (which can correspond to the maximum        frequency), a small step in positive flux and a small step in        negative flux can be taken. “Small” can mean that the shifted        qubit frequency at the new flux values can still be captured in        the same, or a predictable, frequency span as the qubit        spectroscopy measurement used to capture the qubit frequency at        zero flux.    -   2) These first three frequencies can be fitted to a quadratic        model and the fit can be used to extrapolate the frequencies at        a further point in the positive and negative flux directions.    -   3) Now with five frequency points, the frequencies can be        refitted to a quadratic model and extrapolated again.    -   4) The frequencies can be refitted until there are approximately        ten frequencies. Then the tunable transmon frequency model can        be used to extrapolate and update the tunable transmon        Hamiltonian parameters in the database.    -   5) Some of these steps can be repeated if new frequency        measurements are being obtained.        In some implementations, a Ramsey measurement is built, for        example, using one or more of the following operations:    -   1) For T2        -   a) Guess what T2 will be (T2_guess).            -   i) Extrapolate from previous trend, for example, by                using an averaging filter to reduce noise.        -   b) Set the time span from 0 to 4*T2_guess.        -   c) Set the detuning of the reference frame to 1/T2_guess.        -   d) Set the time step to 0.1/T2_guess.    -   2) For frequency        -   a) Guess what the frequency will be.        -   b) Set the time span to an approximately 100 ns window near            zero.        -   c) Set the time step to approximately 1 ns. This can imply a            measurement bandwidth of approximately 100 MHz.        -   d) Set the detuning of the reference frame to approximately            50 MHz away from the guessed frequency.        -   e) This gives sensitivity to frequencies within            approximately 50 MHz of the guessed frequency.

FIG. 7 shows a diagram 700 of a process for flux bias automation. Insome implementations, the process includes performing a set ofmeasurements in a particular sequence within a loop over DC flux biasvalues and with a specific data flow. In particular, diagram 700includes an analysis 702 process, a resonator spectrum model 704, a f₀₁spectrum model 706, a f₁₂ spectrum model 708, and a flux noise model710. Diagram 700 further includes a database 712. Diagram 700 furtherincludes a set flux bias 714 process, cavity frequency spectroscopy 716process, qubit frequency spectroscopy or Ramsey spectroscopy 718process, a power Rabi spectroscopy 720 process, a relaxation (T1) 722process, a Ramsey (τ2) 724 process, and an end loop 726 process.

Some processes shown in FIG. 7 include performing a low-power readoutfrom a low-power cavity spectroscopy 716 and updating the readoutfrequency to a given point relative to cavity peaks associated with thequbit. Additionally, FIG. 7 includes a process of performing a low-powerreadout from a low-power cavity spectroscopy 716. Moreover, FIG. 7 canfurther include determining a resonance frequency f_(r), a qualityfactor (Q_(r)), a readout frequency (f_(ro)), a readout power (P_(ro)),and a coupling parameter χ. The various parameters, including thereadout power and the readout frequency can be saved to the database712.

FIG. 7 includes a process of performing a qubit spectroscopy or Ramseyfrequency measurement 718, for example, to obtain the qubit frequency ata given flux bias. Additionally, a frequency f₀₁, a frequency f₀₂/2, thecircuit bandwidth (or linewidth) Q_(q), the qubit-qubit dispersive shiftζ, and anharmonicity n can be obtained. The various parameters, forexample, the qubit frequency at the flux bias can be saved to thedatabase 712.

FIG. 7 further includes a process of performing a power Rabi measurement720 and identifying the optimal readout quadrature. Additionally, theRabi oscillation rate Ω can be determined. The updated optimalquadrature data can be saved to the database 712. FIG. 7 additionallyshows that T1 can be measured 722 and stored in the database 712.Further, T2* can be measured (using Ramsey technique 724) and stored inthe database 712.

In some implementations, the database 712 can be in communication with aprocessor that can perform or apply one or more of an analysis 702process, a resonator spectrum model 704, a f₀₁ spectrum model 706, a f₁₂spectrum model 708, and a flux noise model 710. The database 712 cansupply the processor and the models described above with variousparameters obtained in processes 714-726.

In some implementations, a calibration process can provide technicaladvantages for operating a quantum computing system. For instance, thecalibration process may provide reliable results by applyingwell-defined criteria for pass/fail during calibration ofsuperconducting qubits. Design expectations may be used to execute anautomated calibration process, providing initial values and the basis ofseveral pass/fail criteria. A calibration routine may be implemented ina manner that is robust to many types of device failure. A computerprogram with a defined experimental procedure may control thecalibration process, which can increase efficiency and consistency whilereducing opportunities for error. In some cases, the calibration processcan be applied to a very large number of qubits simultaneously, whichcan enable large-scale quantum computing in some systems. Thecalibration process may reduce the time used to characterize a deviceand shorten the design-fabricate-measure cycle.

In some aspects, a computer system controls one or several instrumentsto generate or measure signals, and an automated calibration processdetermines one or several control parameters or device characteristicsof a specific device under test. The control parameters and devicecharacteristics can be stored in a database. One or more measurementsteps can be performed. An experimental procedure can define the orderof measurement steps. The experimental procedure can include modularsub-procedures that can be reused or run independently. A measurementstep can further include a computerized routine to extract relevantcontrol parameters and device characteristics. A measurement step canfurther include a computerized routine that determines the “result” ofthe measurement, where the result includes one or more of: a pointer tothe next measurement step in the experimental procedure; a repetition ofthe current measurement with different parameters; a failure conditionwhich terminates the characterization and calibration cycle; or asuccess condition which terminates the characterization cycle.Termination in success or failure can trigger a human-readable alert toa configurable set of people. The alert can be sent via email (e.g.SMTP), instant message (e.g. Skype, IRC, Slack), or otherwise. Theroutine can further include a statistical goodness of fit metric with adefined threshold. The quality of fit metric can include the reducedresidual chi-square statistic, the Akaike Information Criterionstatistic, the Bayesian Information Criterion statistic or another fitmetric. The routine can further include a machine learning algorithmthat has been trained, for example, on human-classified measurementresults from the same system. The routine can further include one ormore statistical goodness of fit metrics with machine learning.

Some of the subject matter and operations described in thisspecification can be implemented in digital electronic circuitry, or incomputer software, firmware, or hardware, including the structuresdisclosed in this specification and their structural equivalents, or incombinations of one or more of them. Some of the subject matterdescribed in this specification can be implemented as one or morecomputer programs, i.e., one or more modules of computer programinstructions, encoded on a computer storage medium for execution by, orto control the operation of, data-processing apparatus. A computerstorage medium can be, or can be included in, a computer-readablestorage device, a computer-readable storage substrate, a random orserial access memory array or device, or a combination of one or more ofthem. Moreover, while a computer storage medium is not a propagatedsignal, a computer storage medium can be a source or destination ofcomputer program instructions encoded in an artificially generatedpropagated signal. The computer storage medium can also be, or beincluded in, one or more separate physical components or media (e.g.,multiple CDs, disks, or other storage devices).

Some of the operations described in this specification can beimplemented as operations performed by a data processing apparatus ondata stored on one or more computer-readable storage devices or receivedfrom other sources.

The term “data-processing apparatus” encompasses all kinds of apparatus,devices, and machines for processing data, including by way of example aprogrammable processor, a computer, a system on a chip, or multipleones, or combinations, of the foregoing. The apparatus can includespecial purpose logic circuitry, e.g., an FPGA (field programmable gatearray) or an ASIC (application specific integrated circuit). Theapparatus can also include, in addition to hardware, code that createsan execution environment for the computer program in question, e.g.,code that constitutes processor firmware, a protocol stack, a databasemanagement system, an operating system, a cross-platform runtimeenvironment, a virtual machine, or a combination of one or more of them.

A computer program (also known as a program, software, softwareapplication, script, or code) can be written in any form of programminglanguage, including compiled or interpreted languages, declarative orprocedural languages, and it can be deployed in any form, including as astand-alone program or as a module, component, subroutine, object, orother unit suitable for use in a computing environment. A computerprogram may, but need not, correspond to a file in a file system. Aprogram can be stored in a portion of a file that holds other programsor data (e.g., one or more scripts stored in a markup languagedocument), in a single file dedicated to the program, or in multiplecoordinated files (e.g., files that store one or more modules, subprograms, or portions of code). A computer program can be deployed to beexecuted on one computer or on multiple computers that are located atone site or distributed across multiple sites and interconnected by acommunication network.

Some of the processes and logic flows described in this specificationcan be performed by one or more programmable processors executing one ormore computer programs to perform actions by operating on input data andgenerating output. The processes and logic flows can also be performedby, and apparatus can also be implemented as, special purpose logiccircuitry, e.g., an FPGA (field programmable gate array) or an ASIC(application specific integrated circuit).

Processors suitable for the execution of a computer program include, byway of example, both general and special purpose microprocessors, andprocessors of any kind of digital computer. Generally, a processor willreceive instructions and data from a read-only memory or a random-accessmemory or both. Elements of a computer can include a processor thatperforms actions in accordance with instructions, and one or more memorydevices that store the instructions and data. A computer may alsoinclude, or be operatively coupled to receive data from or transfer datato, or both, one or more mass storage devices for storing data, e.g.,magnetic disks, magneto optical disks, or optical disks. However, acomputer need not have such devices. Moreover, a computer can beembedded in another device, e.g., a phone, an electronic appliance, amobile audio or video player, a game console, a Global PositioningSystem (GPS) receiver, or a portable storage device (e.g., a universalserial bus (USB) flash drive). Devices suitable for storing computerprogram instructions and data include all forms of non-volatile memory,media and memory devices, including by way of example semiconductormemory devices (e.g., EPROM, EEPROM, flash memory devices, and others),magnetic disks (e.g., internal hard disks, removable disks, and others),magneto optical disks, and CD ROM and DVD-ROM disks. In some cases, theprocessor and the memory can be supplemented by, or incorporated in,special purpose logic circuitry.

To provide for interaction with a user, operations can be implemented ona computer having a display device (e.g., a monitor, or another type ofdisplay device) for displaying information to the user and a keyboardand a pointing device (e.g., a mouse, a trackball, a tablet, a touchsensitive screen, or another type of pointing device) by which the usercan provide input to the computer. Other kinds of devices can be used toprovide for interaction with a user as well; for example, feedbackprovided to the user can be any form of sensory feedback, e.g., visualfeedback, auditory feedback, or tactile feedback; and input from theuser can be received in any form, including acoustic, speech, or tactileinput. In addition, a computer can interact with a user by sendingdocuments to and receiving documents from a device that is used by theuser; for example, by sending web pages to a web browser on a user'sclient device in response to requests received from the web browser.

A computer system may include a single computing device, or multiplecomputers that operate in proximity or generally remote from each otherand typically interact through a communication network. Examples ofcommunication networks include a local area network (“LAN”) and a widearea network (“WAN”), an inter-network (e.g., the Internet), a networkcomprising a satellite link, and peer-to-peer networks (e.g., ad hocpeer-to-peer networks). A relationship of client and server may arise byvirtue of computer programs running on the respective computers andhaving a client-server relationship to each other.

In a general aspect, calibration is performed in a quantum computingsystem.

In a first example, a calibration method includes identifying domains ofa quantum computing system by operation of a control system. The domainscan include domain control subsystems and subsets of quantum circuitdevices in a quantum processor of the quantum computing system. Themethod can further include obtaining a first set of measurements from afirst domain of the domains and storing the first set of measurements ina memory of the control system. The method can include determining, byoperation of the control system, device characteristics of the quantumcircuit devices of the first domain based on the first set ofmeasurements, and storing the device characteristics in a memory of thecontrol system. The method can further include determining to obtain asecond set of measurements from the first domain based on the devicecharacteristics and obtaining the second set of measurements from thefirst domain. The method can include storing the second set ofmeasurements in the memory of the control system, and determining, byoperation of the control system, quantum logic control parameters forthe subset of quantum circuit devices of the first domain based on thesecond set of measurements. The method can further include storing thequantum logic control parameters in a database of the control system foruse in operating the first domain.

Implementations of the first example may include one or more of thefollowing features. The domains can be defined in part by hardware,control logic, physical connections, or software in the quantumcomputing system. The quantum circuit devices of the first domain caninclude qubit devices and readout devices. The control system caninclude a controller (where the controller includes a cache), signalconversion circuitry, a filter, and an amplifier. The control system caninclude an embedded operating system configured to communicate with thedatabase and the controller.

Implementations of the first example may include one or more of thefollowing features. The device characteristics can include resonancefrequencies and coherence times for qubit devices in the first domain.The quantum logic control parameters can include read-out pulseparameters or quantum logic gate pulse parameters for qubit devices inthe first domain. Further, the method can include repeating the firstset of measurements or the second set of measurements based on a successor a failure of a calibration of the first domain of the quantumcomputing system. The quantum logic control parameters can include aparameter for a flux pulse configured to implement a controlled-phaseinteraction. The domain can include at least one flux-tunable qubitdevice. Further, obtaining the first set of measurements can includeperforming a measurement sequence within a loop over multiple flux biasvalues for the flux-tunable qubit device.

In a second example, a quantum computing system includes a quantumprocessor and a control system. The quantum processor includes quantumcircuit devices. The control system can be configured to: identifydomains of the quantum computing system, the domains comprisingrespective domain control subsystems and respective subsets of quantumcircuit devices. The control system can be further configured to: obtaina first set of measurements from a first domain of the domains; storethe first set of measurements in a memory of the control system;determine device characteristics of the quantum circuit devices of thefirst domain based on the first set of measurements; store the devicecharacteristics in the memory of the control system; and determine toobtain a second set of measurements from the first domain based on thedevice characteristics. The control system can be configured to: obtainthe second set of measurements from the first domain; store the secondset of measurements in the memory of the control system; determinequantum logic control parameters for the subset of quantum circuitdevices of the first domain based on the second set of measurements; andstore the quantum logic control parameters in the database of thecontrol system for use in operating the first domain.

Implementations of the second example may include one or more of thefollowing features. The domains can be defined in part by hardware,control logic, physical connections, or software in the quantumcomputing system. The quantum circuit devices of the first domain caninclude qubit devices and readout devices. The control system caninclude a controller (where the controller includes a cache), signalconversion circuitry, a filter, and an amplifier. The control system caninclude an embedded operating system configured to communicate with thedatabase and the controller.

Implementations of the second example may include one or more of thefollowing features. The device characteristics can include resonancefrequencies and coherence times for qubit devices in the first domain.The quantum logic control parameters can include read-out pulseparameters or quantum logic gate pulse parameters for qubit devices inthe first domain. Further, the first set of measurements or the secondset of measurements can be repeated based on a success or a failure of acalibration of the first domain of the quantum computing system. Thequantum logic control parameters can include a parameter for a fluxpulse configured to implement a controlled-phase interaction. The domaincan include at least one flux-tunable qubit device. Further, obtainingthe first set of measurements can include performing a measurementsequence within a loop over multiple flux bias values for theflux-tunable qubit device.

While this specification contains many details, these should not beunderstood as limitations on the scope of what may be claimed, butrather as descriptions of features specific to particular examples.Certain features that are described in this specification or shown inthe drawings in the context of separate implementations can also becombined. Conversely, various features that are described or shown inthe context of a single implementation can also be implemented inmultiple embodiments separately or in any suitable subcombination.

Similarly, while operations are depicted in the drawings in a particularorder, this should not be understood as requiring that such operationsbe performed in the particular order shown or in sequential order, orthat all illustrated operations be performed, to achieve desirableresults. In certain circumstances, multitasking and parallel processingmay be advantageous. Moreover, the separation of various systemcomponents in the implementations described above should not beunderstood as requiring such separation in all implementations, and itshould be understood that the described program components and systemscan generally be integrated together in a single product or packagedinto multiple products.

A number of embodiments have been described. Nevertheless, it will beunderstood that various modifications can be made. Accordingly, otherembodiments are within the scope of the following claims.

What is claimed is:
 1. A method comprising: identifying domains of aquantum computing system by operation of a control system, the domainscomprising respective domain control subsystems and respective subsetsof quantum circuit devices in a quantum processor of the quantumcomputing system; obtaining a first set of measurements from a firstdomain of the domains; determining, by operation of the control system,device characteristics of the quantum circuit devices of the firstdomain based on the first set of measurements; determining to obtain asecond set of measurements from the first domain based on the devicecharacteristics; obtaining the second set of measurements from the firstdomain; determining, by operation of the control system, quantum logiccontrol parameters for the subset of quantum circuit devices of thefirst domain based on the second set of measurements; and storing thequantum logic control parameters in a database on a special purposelogic circuitry controller of the control system for use in operatingthe first domain, wherein the special purpose logic circuitry controllerhas low-latency communication with the quantum processor.
 2. The methodof claim 1, wherein the domains are defined in part by hardware, controllogic, physical connections, or software in the quantum computingsystem.
 3. The method of claim 1, wherein the quantum circuit devices ofthe first domain include qubit devices and readout devices.
 4. Themethod of claim 1, wherein the control system comprises a controller,the controller including a cache, signal conversion circuitry, a filter,and an amplifier.
 5. The method of claim 4, wherein the control systemcomprises an embedded operating system configured to communicate withthe database and the controller.
 6. The method of claim 1, wherein thedevice characteristics comprise resonance frequencies and coherencetimes for qubit devices in the first domain.
 7. The method of claim 1,wherein the quantum logic control parameters comprise read-out pulseparameters or quantum logic gate pulse parameters for qubit devices inthe first domain.
 8. The method of claim 1, wherein the method furthercomprises repeating the first set of measurements or the second set ofmeasurements based on a success or a failure of a calibration of thefirst domain of the quantum computing system.
 9. The method of claim 1,wherein the quantum logic control parameters comprise a parameter for aflux pulse configured to implement a controlled-phase interaction. 10.The method of claim 1, wherein the first domain comprises at least oneflux-tunable qubit device and obtaining the first set of measurementscomprises performing a measurement sequence within a loop over multipleflux bias values for the flux-tunable qubit device.
 11. The method ofclaim 1, wherein the special purpose logic circuitry controller is afield-programmable gate array.
 12. The method of claim 1, wherein thespecial purpose logic circuitry controller is an application specificintegrated circuit.
 13. A quantum computing system comprising: a quantumprocessor comprising quantum circuit devices; and a control systemconfigured to perform operations comprising: identifying domains of thequantum computing system, the domains comprising respective domaincontrol subsystems and respective subsets of the quantum circuitdevices; obtaining a first set of measurements from a first domain ofthe domains; determining device characteristics of the quantum circuitdevices of the first domain based on the first set of measurements;determining to obtain a second set of measurements from the first domainbased on the device characteristics; obtaining the second set ofmeasurements from the first domain; determining quantum logic controlparameters for the subset of quantum circuit devices of the first domainbased on the second set of measurements; and storing the quantum logiccontrol parameters in a database on a special purpose logic circuitrycontroller of the control system for use in operating the first domain,wherein the special purpose logic circuitry controller has low-latencycommunication with the quantum processor.
 14. The system of claim 13,wherein the domains are defined in part by hardware, control logic,physical connections, or software in the quantum computing system. 15.The system of claim 13, wherein the quantum circuit devices of the firstdomain include qubit devices and readout devices.
 16. The system ofclaim 13, wherein the control system comprises a controller, thecontroller including a cache, signal conversion circuitry, a filter, andan amplifier.
 17. The system of claim 16, wherein the control systemcomprises an embedded operating system configured to communicate withthe database and the controller.
 18. The system of claim 13, wherein thedevice characteristics comprise resonance frequencies and coherencetimes for qubit devices in the first domain.
 19. The system of claim 13,wherein the quantum logic control parameters comprise read-out pulseparameters or quantum logic gate pulse parameters for qubit devices inthe first domain.
 20. The system of claim 13, wherein the control systemis configured to repeat the first set of measurements or the second setof measurements based on a success or a failure of a calibration of thefirst domain of the quantum computing system.
 21. The system of claim13, wherein the quantum logic control parameters comprise a parameterfor a flux pulse configured to implement a controlled-phase interaction.22. The system of claim 13, wherein the first domain comprises at leastone flux-tunable qubit device and obtaining the first set ofmeasurements comprises performing a measurement sequence within a loopover multiple flux bias values for the flux-tunable qubit device. 23.The system of claim 13, wherein the special purpose logic circuitrycontroller is a field-programmable gate array.
 24. The system of claim13, wherein the special purpose logic circuitry controller is anapplication specific integrated circuit.